Hardcover ISBN:  9780821802854 
Product Code:  MMONO/144 
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Electronic ISBN:  9781470445614 
Product Code:  MMONO/144.E 
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Book DetailsTranslations of Mathematical MonographsVolume: 144; 1995; 197 ppMSC: Primary 76; Secondary 35;
This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary NavierStokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair onepoint velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.
ReadershipResearchers and graduate students working in mathematical physics and hydrodynamics.

Table of Contents

Chapters

Introduction

Chapter I. Stationary flows of an ideal fluid on the plane

Chapter II. Topology of twodimensional flows

Chapter III. A twodimensional passing flow problem for stationary Euler equations

Chapter IV. The dissipative top and the NavierStokes equations

Chapter V. Specific features of turbulence models

Appendix. Formal constructions connected with Euler equations


Reviews

The book overall treats a number of very special problems … from an interesting perspective.
Mathematical Reviews 
Can be used by researchers and graduate students working in mathematical physics and hydrodynamics.
Zentralblatt MATH


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This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary NavierStokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair onepoint velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.
Researchers and graduate students working in mathematical physics and hydrodynamics.

Chapters

Introduction

Chapter I. Stationary flows of an ideal fluid on the plane

Chapter II. Topology of twodimensional flows

Chapter III. A twodimensional passing flow problem for stationary Euler equations

Chapter IV. The dissipative top and the NavierStokes equations

Chapter V. Specific features of turbulence models

Appendix. Formal constructions connected with Euler equations

The book overall treats a number of very special problems … from an interesting perspective.
Mathematical Reviews 
Can be used by researchers and graduate students working in mathematical physics and hydrodynamics.
Zentralblatt MATH